A displacement based optimization (DBO) method is applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the method as compared to traditional structural optimization. Minimumweight truss sizing problems with various path-independent elastoplastic laws, including elastic perfectly plastic, linear strain hardening, and Ramberg-Osgood models, are investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. To implement the methodology a computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics is developed. Several test problems are successfully solved using the DBO approach and solutions are compared to those available in the literature, demonstrating significant reduction of computational time in comparison to the traditional structural optimization method. In particular, the DBO approach is found to be suitable for truss topology design since the method allows member areas to have cross-sectional areas equal to zero exactly.